Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed...

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 262 feet and a standard deviation of 45 feet. Let X be the distance in feet for a fly ball.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly hit fly ball travels less than 304 feet. Round to 4 decimal places.

c. Find the 80th percentile for the distribution of distance of fly balls. Round to 2 decimal places.  feet

Homework Answers

Answer #1

Solution :

Given that ,

mean = = 262

standard deviation = = 45

a.

X N (262 , 45)

b.

P(x < 304) = P[(x - ) / < (304 - 262) / 45]

= P(z < 0.93)

= 0.8238

Probability = 0.8238

c.

Using standard normal table ,

P(Z < z) = 80%

P(Z < 0.84) = 0.8

z = 0.84

Using z-score formula,

x = z * +

x = 0.84 * 45 + 262 = 299.8

80th percentile 299.8 feet

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